The conventional first principles method to evaluate phonon frequencies of materials at zero temperature is density functional perturbation theory (DFPT) [1]}.
In DFPT calculations, which are based on a harmonic description of the lattice, an imaginary eigenvalue of the dynamical matrix indicates a phonon instability that can point towards a phase transition.
However, DFPT does not include the quantum nuclear effects that are believed to stabilise the paraelectric phase in SrTiO\(_3\)  and therefore wrongly predicts an instability of the FES mode that suggests a phase transition to ferroelectrity [2]}, [3]}, [4]}.
This failure to describe quantum paraelectricity and its influence on the frequency of the FES mode, prevents the application of standard ab initio methods to give a microscopic explanation of recent experiments on quantum criticality and THz induced ferroelectricity in SrTiO\(_3\)  [5]}, [6]}, [7]}, [8]}, [9]}.
<FIGURE>